Related papers: Query Complexity with Unknowns
This paper considers the quantum query complexity of {\it $\eps$-biased oracles} that return the correct value with probability only $1/2 + \eps$. In particular, we show a quantum algorithm to compute $N$-bit OR functions with…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
Vision-Language Models (VLMs) have achieved remarkable progress in complex visual understanding across scientific and reasoning tasks. While performance benchmarking has advanced our understanding of these capabilities, the critical…
Large language models (LLMs) have shown strong capabilities, enabling concise, context-aware answers in question answering (QA) tasks. The lack of transparency in complex LLMs has inspired extensive research aimed at developing methods to…
We consider the problem of estimating a parameter associated to a Bayesian inverse problem. Treating the unknown initial condition as a nuisance parameter, typically one must resort to a numerical approximation of gradient of the…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompass a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token…
Uncertainty estimation has been extensively studied in recent literature, which can usually be classified as aleatoric uncertainty and epistemic uncertainty. In current aleatoric uncertainty estimation frameworks, it is often neglected that…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
It is common practice for data scientists to acquire and integrate disparate data sources to achieve higher quality results. But even with a perfectly cleaned and merged data set, two fundamental questions remain: (1) is the integrated data…
Graphical models have demonstrated their exceptional capabilities across numerous applications. However, their performance, confidence, and trustworthiness are often limited by the inherent randomness in data generation and the lack of…
While it is known that there is at most a polynomial separation between quantum query complexity and the polynomial degree for total functions, the precise relationship between the two is not clear for partial functions. In this paper, we…
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…
The quantum query models is one of the most important models in quantum computing. Several well-known quantum algorithms are captured by this model, including the Deutsch-Jozsa algorithm, the Simon algorithm, the Grover algorithm and…
Quantifying unknown quantum entanglement experimentally is a difficult task, but also becomes more and more necessary because of the fast development of quantum engineering. Machine learning provides practical solutions to this fundamental…
To help a user specify and verify quantified queries --- a class of database queries known to be very challenging for all but the most expert users --- one can question the user on whether certain data objects are answers or non-answers to…
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…
Nowadays, more and more process data are automatically recorded by information systems, and made available in the form of event logs. Process mining techniques enable process-centric analysis of data, including automatically discovering…
In safety-critical applications, language models should be able to characterize their uncertainty with meaningful probabilities. Many uncertainty quantification approaches require supervised data; however, finding suitable unseen…